Tag: curriculum

Nov/Dec ’15 Curriculum

Well, at least this month’s curriculum planning only took 3-4 hours.  I decided to group them together because Dec will be a short month and Nov we will have about 1/2 week off.

I think I covered about half of what I wanted to last month, not too bad.

I can feel the laze starting to set in.  Which means that my presentation calendar isn’t as detailed as it used to be.  I hope it doesn’t really come back to bite me.  On the days when I’m good, it is still very nice to just check the calendar and see what presentation I’m supposed to give.

The kids actually did sing a Halloween song last month and I hope to cover one this month.  We even managed to make some ceramic pumpkins.

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Oct ’15 Curriculum

I spent over 6 hours planning my October curriculum this weekend.

This is the first year I’m doing serious curriculum planning.  It’s the one area that I don’t see a lot of Montessori bloggers post about; how do you go about doing it?  Or maybe I haven’t looked closely.  So I feel like I’m still figuring things out.  What I have realized is that, for my personality, slightly over planning is better than no planning.  When I look back at my Aug/Sept curriculum, we hit about 80% of my lesson plans.  This would not have happened before without planning.

What I am doing now is to do a monthly curriculum planning after deciding on a theme.  With a theme and subject categories, it makes it much easier to tie our studies around that theme.  Then given my one presentation a day schedule, I can schedule these presentations onto a Google Calendar.  Last month, I managed 2-3 presentations a week out of planned 5-6.  Without this schedule, I would probably just do 1-2 a week at most.  It also allowed me to cut down on my curriculum if they don’t fit on the calendar.  Because really, I can only do about 4 topics per subject per month given my 1 subject presentation a week schedule.

Another reason I find planning useful is that it makes me celebrate holidays.  Otherwise it is my default state to do very traditional teaching, as in, sit down, study for hours on end without rest, out of a textbook, despite my desire to not do so.

For October, our theme is Halloween, time, and Timeline of Life.  Not sure what I’m doing with Timeline of Life.  We didn’t spend nearly enough time with Time last month so I wanted to continue this month.  And we’ll use Halloween as a jump off point for our songs, arts and crafts, and practical life.

Math is pretty much the same as last month.  For Chinese, I’m going to try and have both kids learn 100 characters.  We’re now using the Writing with Ease curriculum for Chinese as well.   For English, I hope we’ll make more inroads into the strange phonics that is English.  Montessori has so many interesting presentations for science, I really tried this month to see if I can squeeze it into presentations on top of our Wednesday co-op.  Because I personally find it interesting and amazing how thing all tie together.

When I plan curriculum out on a calendar, somehow I’m able to make peace with the fact that the kids will only really do art related work twice in one month if we’re good and 4 times if we’re super good.  Because I see how many other things we’re doing day to day.  Otherwise, I start feeling that the kids would do better in public school.

Astroboy Thumper
Math
– counting skip counting, 3, 4
– memorization addition/subtraction multiplication memorization 8, 9, 11, 12
– operations addition/subtraction golden beads multiplication/division
– squaring Passing from one square to another
– geometry geometric shapes points and lines
– fractions introduction to fractions
Chinese
– characters Sagebooks Set 2 100 characters
– writing metal insets, components Writing w/ ease, 3 a day, child autum poem for writing, song to write
– words
– songs 月亮代表我的心, 嗚哇嗚哇變, 地球公轉 The Earth goes around the sun 嗚哇嗚哇變
– poems harvest poem harvest poem
– books Halloween related books Day of the Day books?, spooky books
– zhuyin all 37 zhuyin+20 combos practice along with writing
– mechanics Introduction to sentences and phrases
– grammar Introduction to nouns
English
– English sandpaper letters 4 letters Primary phonics set set 4,5
– writing Writing with Ease Week 10 Lesson 2
– mechanics Introduction to periods, sentences and phrases, abbreviation
– grammar Introduction to verbs
– literaray recognizing literary elements, identify themes and plot
– book
Science
– Earth earth’s gravity, earth’s rotation – days and night (related to time & mooN)
– Physical building circuits
– Life B3: Plants vs Animals, B4: life Cycles
– nature of matter solids/liquids/gas classification A3/A4: Air is Substance followup
– Geography Australia Europe
History Personal Timeline, months of the year, clock reading Personal Timeline, BC/AD Timeline
Great Lessons #3-6
Art ceramic stars, colors lesson #2, Halloween pumpkin art Day of the day art?
Elements of Art
Music solfege 一隻青蛙, Halloween related songs (witch, halloween) 古老的時鐘 on piano?
Practical Life Halloween related art or crafts

Science Curriculum: Building Foundations of Scientific Understanding

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Someone once told me that the Montessori Science curriculum is the foundation for elementary.  As in, children learn all the other subjects off of science.  It basically covers from the Big Bang all the way to all things human.  It’s a vast curriculum.  One where you are not expected to cover everything in the albums by 6th grade.

I have 2 albums for science: geography and biology.  Biology covers zoology (animals) and botany (plants).  Geography in a way covers everything else: astronomy, geology, physical geography, chemistry, water, wind, economics, etc.  You are essentially studying the earth and all the fields related to it. One thing they keep telling us during training is: Don’t follow the album sequence in presentation.  However, even many schools do this.  They may decide to do the section on Wind, Water, or human anatomy in upper elementary, and biology in lower elementary.

Especially with homeschooling, I see the varied interests and various questions the children ask and it seems obvious to follow their interests.  However with such a vast curriculum it is hard to know where to start.  I was really to happy to come across the recommendation of a series of books from What Did We Do All Day.  The books are called Building Foundations of Scientific Understanding.  For his K-2 book, he divided scientific knowledge into 4 sections, Nature of Matter (chemistry and the like), Life Science, Physical Science, and Earth Science.  What I like about the book are:

  • It follows my Montessori curriculum.  I have only looked closely at the beginning presentations and it’s basically the same order as what we present in the primary albums.  And the contents are mostly the same as well.
  • But it is WAY more in depth.  The author lists recommended books, how many minutes it takes to present, a guide on how to teach science, follow up activities, etc.
  • In a way, Physical Science is modern science so was not included in our training.  So it’s not in our album.
  • The BEST part is the 2 page chart on the sequence of presentation.  He tells you exactly the prerequisites for each presentations, and sometimes those presentations require other presentations from other sections. 
BFSU
Scope and Sequence!

Last year, Thumper watched a lot of Magic Schoolbus on Netflix and started sprouting scientific facts.  And for awhile I was very confused and wondered, “Why can’t we just watch a lot of TV to learn science?”  I had to have a talk with my fellow homeschooling friend to understand it’s important for the child to also experience science.  I also realized the other important thing is to see how everything is connected.  Biology is connected to chemistry is connected to earth science, etc.  They’re not specific unit subjects to study.  Scientific knowledge, really all knowledge, is not about memorizing little facts but seeing the connections between facts.  And the Montessori curriculum provides a framework through its Great Lessons in tying these things together.   Similarly I feel like this author understands this by that 2 page chart on presentation sequence.  He’s showing me what I need to know in one subject in order to learn about another subject.  Best of all, he’s helping me make sense of my albums.  It’s my one frustration, that there’s no scope and sequence in my album.

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Aug/Sep ’15 Curriculum

I think I’m going just a teeny tiny bit overboard with my curriculum planning.

Yesterday, I came across an old monthly curriculum from Thumper’s preschool, and I realized that I wanted to do something similar.  The great thing about it was that there was a “theme” for the month and the subjects revolved around that theme.  One thing about Montessori (especially in the Sciences) is how everything is related to each other.  For example, if you’re studying fish in science, a child could work on counting fish in Math, or drawing fish in Art.  I’m sure this is not unique to Montessori.  All teachers try to find ways to make the learning process more interesting by tying in books, music, art, etc.

Another reason I wanted to do some detailed planning is that I tend to just have general “plans” that never go anywhere.  I say I want the kids to learn art, but without concrete actionable items I don’t get to it.

So here’s the curriculum I came up with.  My theme for Aug/September is “Mid-Autum Festival, Solar System, Moon, Time”.  If I don’t put the mid-autum festival in, we never celebrate any Chinese or American holidays.  The beginning of the school year is when we typically start with study of the Solar System (because Montessori history/science goes from big to small).  Which is perfect because it ties in with the Mid-Autumn Festival.

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Curriculum for 2015-2016

After weeks of having ideas in my head for what I want to do next year, I finally sat down today and wrote it all down on my google docs. I have no idea how to display a google doc in a non-hosted wordpress website, so I will link to it here.

It is very general.  I looked through the curriculum list from Garden of Francis because her albums are basically my albums except more detailed.  One thing I learned last year was that there are two types of albums, the more AMI bent one, which kind of says expose everything to the kids as they’re interested, with many things happening in 1st grade.  And then the more AMS bent one, which is way more detailed and sequenced slowly, kind of as if kids are starting Montessori as a kindergartener.  For example, my AMI-style album starts with multiplication.  The AMS albums I have seen starts with golden beads or stamp game with addition/subtraction.

Because I am more AMI-style trained, I think I’m more partial to that way of teaching, especially seeing it work in the classroom last year and feeling that giving the child what really interests them makes for great work.  On the other hand, it makes planning really hard and I felt at a loss most of the time.  So it is kind of nice just having the AMS style albums at hand to see the detailed and various presentations you *could* do, to give myself an idea of how I know when a child has mastered a concept.

(Please note that AMI vs AMS is just my interpretation.  I don’t know if it’s true or not.  It’s how I differentiate in my head.)

In any case, with that curriculum list and my own albums, I created a general plan, and then looked through the 2 other AMS album sources I have to fill in any blanks I see.

I looked at my plan from last year and I was surprised to see just how many of my items on my todo list I managed to hit, except for the science part.  For example, I had radicals, components, stroke order all in there and I actually did present some of those.  For Astroboy I had learning to count to 10, 20, and 100, and I hit all those too.  And all without consulting my plan after I wrote it down that one time!

In terms of Chinese, I have quite ambitious goals for both kids.  For Thumper I have:

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Analyzation of Sagebook Character Choices

I have finally come up with how I’m going to choose my next characters.  That took me two blurry eye days and back to drinking coffee.  I know I don’t really need to do things this way.  It would save me so much time to just use a textbook.  For some reason I enjoy the process of analyzing and inputting data.   I also want to be able to keep track of characters learned.  There is obviously another way to do this, when the child practices writing characters, log it in your logbook.  Voila.

Anyways, to come up with the list, first I had to analyze the books and how the characters show up.  It’s really fascinating and took me down different paths.  I learned a few things on how the characters are introduced.

  • Progression of character difficulty:  As the series progressed, more and more characters from second “grade” and beyond showed up.  I say “grade” because they’re saying 3000 characters by 6th grade.  The first “grade” has 508 characters.  It’s really 510 because they added but never introduced 一 and 完.  Second grade was 716!  By series 5, about 50% was from second grade.  Often, the higher the grade level, the more strokes and more abstract meaning.  Obviously this is how most people teach characters.  But what I like about Sage is that they do introduce characters from higher grade level early on.  Many of them are used in children’s books.  Oh! and I also realized, going through all 3000 characters, that if you can get to about 3rd grade, which is 1866 characters, you’re pretty set.  Those seemed to have characters I would deem important to know the meaning of.
  • Division by grammar functions: There is an even division of grammar characters.  For example, they will introduce nouns, verbs, and the other “stuff”; adjective, adverbs, conjunction, interjection, preposition, particles, in a pretty even distribution.  I learned that really, you cannot look at a Chinese character and say it is a verb, a noun, or an adjective.  They combine with other characters to form a word and those words then have grammar functions.  But, I tried anyway because I did not want to look up how each word was introduced in Sage and then define them.  I don’t think I’m too far off though.
  • Words:  Related to grammar functions, I think I will need to introduce different words based on same character as the books in the series progresses.
  • Division by Theme: Characters in a series are grouped by theme.  For example, the Blue series introduces pronouns, direction, numbers, verbs, and helping verbs.  Red series, the last one, introduces school, family life, community life, social life, science, social studies, personal relationships.  Within each book in the series, characters from each theme are introduced.  Looking at the themes, you can see it kind of goes from people outward to community and school life.
  • Character Review:  Because a few characters from each theme is introduced in each book, the child reviews previous characters from the previous book when they introduce new characters in the same theme.  This is in addition to reviewing characters from the chapters you just learned.  I imagine this is the hardest part I’m going to have when I come up with sentences.
  • Other:  Since each character could have multiple meaning depending on words it’s used in, the series makes sure to introduce these words.  As the series progresses, the number of characters per sentence gets longer.   They also introduce other grammar points like questions.  In the beginning most of the sentences are based in reality.  They introduce children’s stories in the pink series (the monkey and pig).

Anyways, I calculated stats on grade level and grammar and decided that my characters will be chosen by themes as well.  Given that subject vocabulary is introduced early on in Montessori curriculum, I decided that I would focus on subjects such as geography, zoology, botany, and solar system.  But once I started choosing the characters, I realized it was really hard to choose!  I had to make sure there is a good distribution of grade level as there are still 200+ characters from 1st “grade” after 500 characters.  Then each series only really gives you about 50 nouns.   Then I have to make sure there is a good distribution of grammar functions, which means I have to look up the common words used for that character, knowing that I would need to introduce different words in the series based on each character.   I also wanted to introduce Chinese counters, conjunctions, colors, math concepts like 個十百千.  So many concepts still not introduced after 500 characters!

i had to narrow my theme for the 6th set given all these constraints.  On the other hand, it does provide me with themes for the 7th series.  Once I picked my 100, the problem comes with order of introduction.  I made a first pass, then as I started writing sentences, kept running into the problem of characters not being introduced yet.  Yikes!  Like the ubiquitous 它.  I guess they got around that problem by using 他.

What did I pick?

All this to say, for the next set I aim to have about 50% second grad characters, followed by first grade, and third grade.  My current breakdown is:

  • Adjective 13
  • Conjunction 4
  • Noun 47
  • Preposition 1
  • Verb 29

My theme will be Math Counters, Geography, and Zoology.   I know it will change as I progress because I will find characters I need that’s not on my list.  But it gives me a starting point.  Another problem I’m having is, how hard to I make the sentences?  Do I write for a 5 year old or 7 year old?

Lastly, as usual, one project leads to another and another.  I kept thinking as I went through the characters that I really need to introduce radicals and counters.  So for sure radicals is next.  I feel like the characters are going to start getting confusing because of their similarities and it’s time to introduce radicals to help with meaning.

Learning the next 500 Chinese characters

Let it be known that I like to take the long and painful way to do something.

I’ve been spending the last 2 days going through the list from a Hong Kong website of the 3000 characters one can learn.  This research website looked at what characters they teach in China, Hong Kong, and Taiwan, analyzed it to determine word frequency, difficulty level, character components, and radical.  They even sent out a survey to teachers to ask them to gauge difficulty level.  The result are 4 different lists of characters, sorted by difficulty level, grade level, frequency level, and radical.

On the website, you can generate you own list of characters you want to learn by inputting how many characters you want to learn by grade level.  Because the characters are gifs, I’ve been painstakingly typing in each character and its pinyin.  I’m very close to being finished.  I’ve already finished mapping all the Sagebook characters to the list from the website.What I plan to do is to generate the next 500 characters once I’m done, by adding in grammar function and analyzing how Sagebook came up with their list.

If you just tell the website to show you how many characters to learn each grade, it’s actually split up this way:

Grade Characters Total %
1st 508 508 75%
2nd 716 1234 91%
3rd 632 1866 96.4%
4th 558 2424 98.3%+
5th 412 2836 99.0%+
6th 172 3010 99.2%

Quite different from Taiwan, where you would reach 91% by 3rd grade instead.

I noticed a few things while compiling the list:

  • They’re suggesting that you can learn 3000 characters by 6th grade!  This is totally different from the number of characters you will learn in Taiwan by the end of 6th grade.  You learn 2400 characters for reading and 1800 for writing.   But as you can see from my link, a 600 character difference only moves you up 1% point.  Because of this, I’m going to try and stick with 2400 characters.
  • I actually know most of these characters!  Given that I had a 4th grade level education from Taiwan, which equates to 1200 characters for writing and 1600 for reading, that is totally not bad at all.
  • Working with 3000 characters, my eyes started to glaze after awhile and I started getting confused on what the meaning of each character is.  I noticed that the way I am able to type a character out is to type a word that I know which uses the character.  So characters really should not be learned individually, but rather as part of a word.  Thumper has been relying on her knowledge of the spoken language to learn her characters.  But going forward, I will have to introduce words as well.  Of course the genius of Sagebooks is that they do introduce the words in the sentences you read.  But I will probably need supplemental material as the vocabulary gets more hard and abstract.
  • I also noticed that Sage does not teach just the characters that are listed as first grade level.  They have :
    1st 327
    2nd 147
    3rd 23
    4th 3

    In the 3rd and 4th grade level words, many are animal words.  As I type away, I see at each grade level, there are words introduced that are of high frequency and others of low frequency.  But, these low frequency words are often words that you would encounter if your’e studying science.   Also, it’s clear they like to introduce characters with low strokes, though it may not necessarily be used often.  For example, 卜.  

    I’m thinking hard now about this.  What characters do I think Thumper would need as she studies science.  Or do I pick words just from first grade and go up, assuming that she will learn the other characters elsewhere.  It’s evident that the way we ought to learn it is to really teach characters that we will encounter in day to day study and not emphasize too much on the grade level it appears in.  There really is no rhyme and reason to what characters you study first in the first few grades.  And you will do well if you study the characters you encounter during your study, as really those ARE your most frequent characters for you….

Hoepfully I will have a list in the next few days, of the next 500 characters…

Chinese Characters by Grade Level

One of the anxieties for me is wondering if the kids are hitting “grade level” in their Chinese characters knowledge.  In the past teachers have refused to tell me, citing reasons like, “They may know it today during the assessment but not know it tomorrow.”  Or, “They may recognize a character but not know how to write it or use it.”  While this is very true, and in fact it’s a problem I see daily with Astroboy, I generally hate it when people don’t want to give me estimates.  THERE IS ALWAYS A RANGE!  Seriously.  Because obviously my child doesn’t know 10000 characters (is there even that many in Chinese?), nor do they know 1000 (it would take longer than 2 years for most children).  To me, it also illustrates the distrust between parents and teachers.  Somehow I’m going to take this info and try to whip my kids into learning more characters faster or accuse them for not knowing enough.  Okay, I will stop ranting now. There is a list published in a research paper of number of characters children will be presented for reading and writing by each grade level in Taiwan.  This is expected number of characters to be introduced.  It does not mean your child will know this many.  But it gives you a good general idea of where your child is vs a child in Taiwan.  Or plan your curriculum.

 Grade Level  Reading (characters / words)  Writing (characters / words)
 1st grade  400 / 600   300 / 400
 2nd grade  800 / 1200   600 / 800
 3rd grade  1200 / 1800   900 / 1200
 4th grade   1600 / 2400  1200 / 1600
 5th grade   2000 / 3000  1500 / 2400
 6th grade   2400 / 3600   1800 / 3000

There is a character vs word component because knowing a character is only half way, since characters are usually used to compose words; e.g. two characters combined.  For each writing level, you’re expected to be able to make a sentence with said character, know when this character should be used.  The same knowledge applies to words you can write. I hear the standards are different in China.  You know a lot more characters by the end of first grade.  But no time to research that right now.  For me, it’s difficult enough in the U.S. to learn this many for each grade level.  No need to feel even more anxious by comparing to China. This website lists frequency character coverage.  I don’t know if it’s based on Traditional or Simplified Chinese though.  Anyways, using this chart we have:

  • 400 = 70%
  • 800 = 85%
  • 1200 = 91%
  • 1600 = 95%
  • 2000 = 97%
  • 2400 = 98%

Looking at this table, it seems that you should be able to read pretty well after 3rd grade.  I’m assuming after 4th or 5th grade, you’ve seen enough characters to really be able to guess at the meaning and pronunciation of new characters you don’t know. For the Sagebooks, this means that it only takes you to 1st grade level and we really need another 500-700 to reach 3rd grade level.  For us, IF we get through the Sagebooks by the end of May like I planned, we’re on track for first grade level.  I guess I better get started on planning what to do with the second 500 characters!   If I want to reach 300 character writing proficiency, we also need to cover up to the Orange Series in Sagebooks.  This means about 20 characters a week.  I’m not sure it is doable.  Though technically Thumper already knows how to write a lot of these characters already.  I just want her to be able to write it properly.

Singapore Math vs Montessori Math

It is quite overwhelming the sheer number of math programs out there for homeschoolers.  Though we already use Montessori math, I got side tracked into cursory looking at the different programs this morning in my quest for math skyscrapers.

What’s Singapore Math?  The only thing I know about it is the review from Cathy Duffy and the free worksheets I looked through quickly.  What jumps out at me from her review are:

  1. It’s a program that teaches children math from concrete, to pictorial, then abstract.  Sounds like Montessori Math.
  2. Concepts are taught thoroughly and sequentially rather than in a spiral.  So once a concept is covered it isn’t covered again except in review.  Montessori Math is more a more spiral approach I think.
  3. The program requires one-on-one teaching.  Not Montessori at all unless they mean that the concept is taught one-on-one and then the children work on it.  Montessori kind of emphasizes the working and learning by yourself part.

I got a headache looking at the worksheets.  I was reminded of the pages and pages of worksheets I did as a child, which often has NO BEARING on math in real life.  I know people say that Singapore Math’s strong point is in how it relates to real world problems.  But looking at the worksheets, often my confusion is on interpreting what the math question is trying to say.  However, they did illustrate concepts that I don’t see in Montessori Math concrete materials.

From Singapore Math I jumped to this listing of homeschool math curriculum overview.  It’s nice seeing it in one page.  A forum thread I came across elsewhere noted that Math-U-See, Shiller Math, and one more all came out of Montessori.  Apparently the “founders” trained with her or her disciples.  Many of these work with the concept of concrete to abstract. Someone also said that Singapore Math is based on Montessori.  I can see that from the point of going from concrete to abstract.  But this idea of teaching math isn’t copyrighted; I’m sure lots of other people have the same idea.  Except maybe Maria beat them by about 100 years.

Singapore Math is super nice to have because it really lays it all out there for you, the math concepts you need to cover, broken down in specific units.  For example, I saw problems for adding 10,000 to a number, or for learning how one equation is same as another, or adding one or subtracting just one from a number.  Very detailed concepts.  Whereas in Montessori, it’s just divided into addition of 4 large numbers, and memorization of addition.  I don’t know if Thumper understand how easy it is to just add a 1000 to a number in an abstract way.  And these are worksheets for 1st graders.  Speaking of Singapore Math, here is a link to free Singapore math material.

So I think people choose programs like Math-U-See or Singapore Math because the curriculum IS laid out for you, in a workbook format.  You know you’re done when you finish the workbook.  It’s much easier to stick an addition worksheet in front of Thumper to see whether or not she has mastered the concept.  It’s harder having her pull out equations from a drawer or generate her own, even though those are more interesting for her to work with.  In addition, while math is sequential, the freedom of choice and the way multiple materials cover the same concepts or review previous concepts can be overwhelming for people who are used to a very sequenced and ordered way of learning (ME!).  It is only human nature that we want to categorize and order things (curriculum in this case).  But for now I’m going to stick with Montessori math, maybe using Singapore Math workbooks as a supplement to see what other concepts I need to teach.  I know Montessori math doesn’t necessarily cover all state standards.  Part of the reason I’d been searching is I learned through worksheets.

But, if Montessori math is the precursor to many of these other math programs, then why not use it.  There is no reason to use materials that have been redesigned and thus lose some of the indirect methods math is taught concretely.  For example, I see the Shiller math concrete materials don’t color code the place values (unit bead, ten bar, hundred square, thousand cubes).  The only thing of course is cost.  The materials are not cheap for homeschoolers.

I never did find my math skyscrapers, which are these drawers of equations to children to work through.  Onward to the search!